For the right triangle shown, the lengths of two sides are given. Find the third side. Leave your answer in simplified, radical form.

Step-by-step explanation:

For this exercise you need to apply the Pythagorean Theorem. This is:

Where "h" is the hypotenuse of the Right triangle and "l" and "m" are the legs.

In this case, you can identify that:

Knowing these values, you can substitute them into  :

Now you must solve for "c":

Evaluating, you get:

To simplify the result:

- Descompose 32 into its prime factors:

- By the Product of powers property, you know that:

- Make the substitution:

- Finally, knowing that , you get:

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

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